Finite Group DatabasebetaFinite Group Databasebeta| order | 1152 |
| nilpotency class | 2 |
| isoclinism | isoclinic class of #3484 |
| automorphism | ? |
| homology | Abelianization (H1) = C25×C9 · Schur multiplier (H2) = C29 |
| direct product | C9×#3489 |
| subgroup | G/H | |
|---|---|---|
| center | C22×C9 | C25 |
| commutator | C22 | C25×C9 |
| Frattini, socle, cosocle | C22×C3 | C25×C3 |
| prime radical | C3×#3489 | C3 |
| LCS | G ▷ C22 ▷ C1 | |
| UCS | C1 ◁ C22×C9 ◁ G | |
2283 conjugacy classes of subgroups.
| minimal degree | μ(G) = 29 |
| transitive degree | μt(G) = 288 |
A minimal faithful permutation representation — 5 generators on 29 points:
(1,2,3,4,5,6,7,8,9)(11,13)(14,15,19,20)(16,22,24,17)(18,26,27,21)(23,25,29,28);(15,20)(17,22)(21,26)(25,28);(10,11)(12,13)(14,16)(15,17)(18,23)(19,24)(20,22)(21,25)(26,28)(27,29);(14,17)(15,16)(18,25)(19,22)(20,24)(21,23)(26,29)(27,28);(14,18,19,27)(15,21,20,26)(16,23,24,29)(17,25,22,28)396 conjugacy classes — view the full character table.
Construct this group in GAP via the SmallGroups library:
gap> SmallGroup(1152, 2221);